Technical Field
The present principles are directed to linear faraday induction generators as well as electrokinetic seawall apparatuses that employ linear faraday induction generators to dissipate ocean wave kinetic energy.
Description of the Related Art
Seawalls are widely used to protect fragile beaches, coastline, and coastal structures from the enormous power and energy of ocean waves and to provide areas of calm water for shipping and recreational purposes. Waves impact upon a seawall, of which there are basically two principal types—type 1 seawalls of uniform thickness with a level exposed face that is perpendicular to the oncoming ocean waves, and type 2 seawalls whose ocean exposed surface is concave upward with a base of significant greater thickness than at its summit. In either case, the waves collide violently with the seawall, which then dissipates the wave energy through frictional losses into useless heat. Seawalls of the first type suffer from the problem that some of the wave energy is reflected producing extremely violent and undesirable standing waves in front of the seawall. Seawalls of the second type, developed to avoid the standing wave problem, suffer from the fact that the curved exposed surface suffers from increased cumulative damage with shortened lifespan as that type of seawall has to absorb all of the wave energy rather than reflecting a portion of it back toward the ocean in the direction of the original wave propagation. In either case, tremendous amounts of energy is wasted and lost as frictional heat and turbulence.
This large amount of undesirable wave kinetic energy is capable of being converted into electrical power. In an effort to mitigate the effect of climate change from carbon emissions from fossil fuel production, other alternative sources of energy, which include wind, hydrogen, solar, nuclear, cellulosics, geothermal, damming, hydroelectric, tidal current, and ocean wave, are now being explored to supply energy requirements for modern industrialized societies. Ocean wave energy in particular has been investigated for possible use as far back as 1799 with the first known patent, and since then, many patents have been issued in an attempt to tap an estimated 1 TW (Terawatt) to 10 TW of power contained in deep water wave power resources of which, by one estimate, 2.7 TW is potentially practical to tap, thereby providing a significant percentage of the planet's power consumption of 15 TW. With existing technology, however, only about 0.5 TW could in theory be captured.
Energy and momentum is imparted to the surface layer of ocean by winds blowing across its surface by virtue of the shearing frictional forces of the wind against the water surface. This transfer occurs when the wave produced as a result of this interaction propagates across the surface at a slower velocity than the wind. This wind ocean system is called the “wind sea state.” A given amount of energy transferred per unit of time will produce a wave whose eventual height will depend on 4 factors: wind speed, the duration of time the wind has been blowing, the distance over which the wind excites the waves (known as the fetch), and the depth and topography of the ocean. Once the wind ceases to blow, these wind generated waves, called ocean surface waves, continue to propagate along the surface of the ocean in the direction of the wind that generated them. The visual distortions that are seen and indicate the presence of such waves are called swells. Because of the restoring force of gravity (hence, ocean waves are known as surface gravity waves), the waves continue to propagate after the wind has ceased blowing, leaving their point of origin as they travel through a viscous medium with a given density, namely ocean water. The energy and momentum associated with an ocean wave front is largely a surface and near surface phenomenon. In deep water, water molecules follow circular motion paths, while in more shallow water, the motions are elliptical. In water depths equal to half the wavelength (the distance between successive wave crests), this orbital motion declines to less than 5% of the motion at the surface. Because of this phenomenon, energy transfer by propagating ocean waves occurs at and just below the surface of the ocean. Furthermore, the momentum associated with this kinetic energy of motion is both linear, reflecting the momentum imparted to the water's surface through wind drag forces, and angular, given by the fact that the wind applies shearing forces to the water at an angle to its surface.
There are two wave velocities associated with ocean wave phenomena, the phase velocity and the group velocity. The phase velocity measures how quickly the wave disturbance propagates through the ocean. It refers to the velocity of each individual wave that propagates across the ocean. However, many waves together may contribute to a summation wave, called a wave group that in itself propagates over the ocean at its own separate velocity. It is the velocity of the wave group, or summation wave, that measures the speed at which energy is transferred across a given section of ocean. Power and energy is transported at and just under the ocean surface at the group velocity. In deep water, the group velocity is equal to one half the phase velocity whereas in shallow water, the group velocity is equal to the phase velocity, reflecting the fact that the phase velocities of all of the individual waves decrease as they approach shallow water in the vicinity of a coastline. Since the energy, momentum, and power contained in a wave remain constant (less frictional losses) as the individual waves approach the coastline, the height of the wave must increase as its base slows, until it becomes unstable causing the wave to fall over itself, a process call breaking. The process of a wave impinging upon a coastline causes all of its stored energy to be released as frictional heat resulting in the undesirable effects to the coastline. The seawall intercepts the wave fronts prior to the breaking process and dissipates the energy instead. Also, waves with the longest wavelengths usually have the highest wave heights, travel the fastest in the ocean, and arrive ahead of waves with shorter wave lengths, as seen with the long high swells observed several days prior to the arrival of a hurricane. These waves carry the greatest amount of energy and are the most harmful to beaches, coast lines, and the life expectancies of seawalls.
The power as given by watts per unit length of wave front transmitted through a plane vertical to the plane of propagation (ocean surface) and parallel to the wave crest front is dependent on the product of the square of the “significant wave height” in meters and the period of the wave in seconds, with the period being the reciprocal of the frequency, which, in turn, varies inversely in a complex function to the wavelength and ocean depth. The height of the wave is defined as the vertical distance between the crest and succeeding trough and it is equal to twice the amplitude of the wave. The “significant wave height” is a statistical average of the heights of the one third of the waves with the highest heights measured during a specified measured time interval of 20 min to 12 hours. The power being transmitted by the wave is known as the “wave energy flux” or “wave power” and it is given by the following equation:
                    P        =                                            ρ              ⁢                                                          ⁢                              g                2                                                    64              ⁢                                                          ⁢              π                                ⁢                                    H              t                        2                    ⁢                      T            e                                              Eq        .                                  ⁢        1            where,                P=Wave energy flux (wave power), Watts/meter (W/m) of advancing wave front=Joules/sec/meter (J/s/m)        ρ=Density of water, 1000 kg/m        Ht=“Significant wave height”=average height of highest one-third of waves measured in a given time interval in meters        Te=Period of wave in seconds        g=Gravitational acceleration, 9.8 m/sEquation 1 can be approximated by the equation:P≈0.5Ht2Te  Eq. 2where P is in Kw/m        
Power and energy get transported horizontally at and just under the surface of the ocean at the group velocity. The above equations calculate the power available in gravity ocean waves, and the energy associated with that power may be calculated as well from linear wave theory, and the thermodynamic principle of the equipartition theorem, applied to a system where the restoring force of gravity causes an ocean wave to function as an harmonic oscillator in which half of its energy on average is kinetic and half is potential. The total average density of energy in Joules per unit of horizontal area of ocean surface in meters (J/M) is given by:
                    E        =                              1            16                    ⁢          ρ          ⁢                                          ⁢                                    gH              t                        2                                              Eq        .                                  ⁢        3            where,E=Average mean density of gravity ocean wave energy at and just below the ocean surface, J/m2.For the following equations below,Cg=Group velocity (wave envelope velocity), m/s,−energy propagation velocityCp=Phase velocity, m/s,−individual wave front propagation velocityA=Amplitude of wave—one half the height, in meters, the vertical distance from crest to succeeding trough.
This power (and energy) gets transported horizontally in the direction of wave propagation at the group velocity. In addition, this power, for waves traveling in sufficiently deep water that the depth, h=½λ, may be calculated by:
                    P        =                  EC          g                                    Eq        .                                  ⁢        4                                where        ,                                                                      C          g                =                              g                          4              ⁢              π                                ⁢                      T            e                                              Eq        .                                  ⁢        5            
Equations 3 and 5 placed into equation 4 gives equation 1, and therefore, the approximate wave power equation, equation 2, which measures the maximum available wave power or wave energy flux that can be extracted by an ocean wave extraction device:
  P  =                    (                              1            16                    ⁢          ρ          ⁢                                          ⁢                                    gH              t                        2                          )            ⁢              (                              gT            e                                4            ⁢            π                          )              =                            ρ          ⁢                                          ⁢                      g            2                                    64          ⁢                                          ⁢          π                    ⁢                        H          t                2            ⁢              T        e            
The efficiency of the wave energy dissipation device whose interception wave surface interface is of length L is given by:
                              E          f                =                              P            ext                    PL                                    Eq        .                                  ⁢        6            where,
P is given by Eq. 1 or as a good approximation, Eq. 2
Ef=Efficiency of the wave energy dissipation device
L=Wave extraction device—wave interception interface length in meters
Pext=Measured electrical power extracted from the device in watts
Finally the generated electrical power density, Pd, can be computed to measure the density of power generation by the device:Pd=Pext/V  Eq. 7:where,
Pd=Generated power density, W/m3 
V=Volume of the energy dissipating device, m3 
For illustrative purposes, a calculated example describing the energy in an ocean wave is provided:
A vertically oriented cylindrical shaped power generating device of diameter 11 meters and height 44 meters is placed floating so that its diameter is parallel to the direction of the arriving wavefront and perpendicular to the direction of propagation of the wave. Further, it is located in deep water a few kilometers off the coast and encounters waves with a height (“significant wave height”) of 3 meters and a wave period of 8 seconds. Using Eq. 2 to solve for P, we obtain:
  P  ≈            (              0.5        ⁢                  KW                                    m              3                        ⁢            s                              )        ⁢                  (                  3          ⁢                                          ⁢          m                )            2        ⁢          (              8        ⁢                                  ⁢        s            )        ≈      36    ⁢          KW      m      36 Kw per meter of wavelength incident on the device over an impact length of 11 meters or 396 Kw in total power. The device produces 150 Kw. Its efficiency is 150 Kw/396 Kw or 39% (from Eq. 6). In addition, given that the device is a cylinder of diameter 11 meters and height 44 meters, where its volume is V=πr2h or 4180 m3; the power generating density Pd=150 Kw/4180 m3=0.36 W/m3 or 360 mw/m3 (from Eq. 7).
Note that because of the dissipated ocean wave energy extracted as electrical energy by the device, the wave train in back of the device will be larger than the attenuated wave front in front of the device. Also, the available wave energy flux increases linearly with the period of the wave but exponentially with the square of the height which produces several effects. Storm waves of great height will destroy such wave energy dissipating devices. For instance, if an approaching storm led to waves of 15 meters high with a period of 15 seconds impacting the device, the device would have to deal with a wave energy flux of 1.7 MW/m of wave impact surface on the device with a total wave energy flux of 18.7 MW. Also, even if the device has excellent survivability, the efficiency of the device will go down drastically if the waves impacting upon it are significantly higher than the height with which the device was designed operate.
Thus, all such ocean wave energy dissipating devices extracting the energy as electrical power should be reasonably efficient through a wide range of ocean wave sizes. It should be durable and have reasonable maintenance requirements as would be the case in a seawall of a conventional nature that is made out of concrete, steel bulkhead, or heavy boulders stabilized by some means.
The prior art technology has made use of systems including and involving pistons and pumps using hydraulic fluids and water, spinning turbines, oscillating water columns to produce air pressure changes driving hydraulic or turbine systems, water intake water elevators with downhill hydroelectric flow turbine systems, linear magnetic arrays coupled to oscillating coil assemblies, and piezoelectric wave pressure to electrical energy transducers. All of these technologies have been considered or have been attempted to be used in extracting electrical energy from ocean wave energy.